What is the (n)th term of the sequence (3,6,11,18,27,\ldots)?
Answer and explanation
Correct answer: \(n^2+2\)
The consecutive differences are 3, 5, 7, and 9, which are successive odd numbers. This indicates a rule involving \(n^2\). To obtain the first term 3 when \(n=1\), add 2 to \(1^2\); hence \(a_n=n^2+2\). Checking: for \(n=2\), it gives 6, and for \(n=3\), it gives 11. Option A gives 2 as the first term, so it is incorrect. Exam tip: For a quadratic sequence, inspect the first and second differences to identify the rule.
Frequently asked questions
What is the correct answer to this question?
\(n^2+2\)
Why is this the correct answer?
The consecutive differences are 3, 5, 7, and 9, which are successive odd numbers. This indicates a rule involving \(n^2\). To obtain the first term 3 when \(n=1\), add 2 to \(1^2\); hence \(a_n=n^2+2\). Checking: for \(n=2\), it gives 6, and for \(n=3\), it gives 11. Option A gives 2 as the first term, so it is incorrect. Exam tip: For a quadratic sequence, inspect the first and second differences to identify the rule.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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